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Difficulty: HardAssumptions in Conditional Logic

A municipality is eligible for the Federal Green Grant only if it has successfully reduced its overall carbon emissions for three consecutive years. Oakhaven recently redirected a large portion of its public transit funding to highway expansion, a policy decision that invariably prevents any reduction in local carbon emissions. Therefore, Oakhaven will not be able to revitalize its downtown commercial district.

Which one of the following is an assumption required by the argument?

  1. Revitalizing a downtown commercial district requires a municipality to be eligible for the Federal Green Grant.Answer
  2. B
    Any municipality that is eligible for the Federal Green Grant will successfully revitalize its downtown commercial district.
  3. C
    If a municipality is unable to revitalize its downtown commercial district, then it must not be eligible for the Federal Green Grant.
  4. D
    A municipality can successfully reduce its overall carbon emissions only if it is eligible for the Federal Green Grant.
  5. E
    Oakhaven would have been able to revitalize its downtown commercial district provided that it had not redirected its public transit funding to highway expansion.

Answer

The assumption required by the argument is that revitalizing a downtown commercial district requires a municipality to be eligible for the Federal Green Grant.
The argument establishes that Oakhaven is ineligible for the Federal Green Grant due to its failure to reduce carbon emissions. It then concludes that Oakhaven cannot revitalize its downtown. For this conclusion to logically follow, being ineligible must guarantee the inability to revitalize (Ineligible → Cannot Revitalize). The contrapositive of this conditional relationship is that revitalizing requires eligibility, which is exactly what the correct statement provides.

Step-by-Step Solution

1
Translate the first premise into conditional logic.
Eligible for Grant → Reduced Emissions
To establish the baseline requirements set by the grant policy.
2
Evaluate Oakhaven's actions based on the second premise.
Redirected Funding → Did NOT Reduce Emissions
To determine Oakhaven's factual status regarding the grant requirements.
3
Combine the premises to deduce Oakhaven's grant eligibility.
Because Oakhaven did not reduce emissions, it is NOT eligible for the grant (Modus Tollens).
To find the ultimate logical consequence of Oakhaven's policy decision.
4
Identify the logical gap between the synthesized premise and the conclusion.
Premise fact: Oakhaven is NOT eligible. Conclusion: Oakhaven CANNOT revitalize downtown. The gap is: NOT eligible → CANNOT revitalize.
To pinpoint the exact assumption required to make the argument logically valid.
5
Formulate the contrapositive of the missing link to find the correct answer.
The contrapositive of 'NOT eligible → CANNOT revitalize' is 'Revitalize → Eligible' (Revitalizing requires eligibility).
Because correct answer choices for conditional assumptions frequently appear in their equivalent contrapositive form.

Key Concept

Assumptions in Conditional Logic requires bridging the gap between established premises and the conclusion using strict necessary and sufficient conditions, often relying on the contrapositive of the missing link to formulate the correct answer choice.
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Topics

Assumptions in Conditional Logic

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